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Response time has attracted increased interest in educational andpsychological assessment for, e.g., measuring test takers' processing speed,improving the measurement accuracy of ability, and understanding aberrantresponse behavior. Most models for response time analysis are based on aparametric assumption about the response time distribution. The Coxproportional hazard model has been utilized for response time analysis for theadvantages of not requiring a distributional assumption of response time andenabling meaningful interpretations with respect to response processes. In thispaper, we present a new version of the proportional hazard model, called alatent space accumulator model, for cognitive assessment data based onaccumulators for two competing response outcomes, such as correct vs. incorrectresponses. The proposed model extends a previous accumulator model by capturingdependencies between respondents and test items across accumulators in the formof distances in a two-dimensional Euclidean space. A fully Bayesian approach isdeveloped to estimate the proposed model. The utilities of the proposed modelare illustrated with two real data examples.

A Latent Space Accumulator Model for Response Time: Applications to Cognitive Assessment Data